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%I #3 May 11 2007 03:00:00
%S 1,-1,3,-1525,615881,-3058641,38800188510523,-3213747182969063,
%T 100462329712125,-43865443313064357090353257,
%U 4543042335221166932765440567147,-103986681387361620043171941
%N Numerators of coefficients in a series for the inverse of harmonic number H(x).
%H David W. Cantrell, <a href="http://groups.google.com/group/sci.math/msg/0926db8773d69b81">Inverse of Harmonic Numbers</a>
%e With InvH(x) being the inverse of H(x), x > 0, an asymptotic series for InvH(x) + 1/2 is u - 1/(24u) + 3/(640u^3) - 1525/(580608u^5) +-... where u = e^(x - g) and g is Euler's gamma constant.
%t n = 12; coeffs = InverseSeries[Exp[Series[HarmonicNumber[x - 1/2], {x, Infinity, 2n - 1}] - EulerGamma]][[3]]; Table[Numerator[coeffs[[2i - 1]]], {i, 1, n}]
%Y Denominators given in A118051. See also A002387.
%K frac,sign
%O 0,3
%A David W. Cantrell (DWCantrell(AT)sigmaxi.net), Apr 08 2006
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